Road Network

The Oklahoma City MSA contains a road network that has developed akin to many cities in the United States. Downtown OKC, which is the oldest part of the MSA, largely follows a grid pattern. As the network moves towards the periphery this street network design changes. The network becomes much more sparse and transitions to a less uniform curvilinear network.

Road Network Summary Statistics

Road classifications are determined by Open Street Maps, from which we extracted our road network.

• Primary roads: 438.3 miles
• Secondary roads: 982.2 miles
• Tertiary roads: 1550.4 miles
• Trunk roads: 299.0 miles
• Links/Centroid Connectors: 3306.2 miles

Estimating Trip Productions

To generate trip production estimates for our model, we ran linear regressions using observed trip counts by purpose (home-based other, home-based work, and non-home-based) as the dependent variable, and four household characteristics pulled from American Community Survey data as the predictors. The census variables we used for these regressions differed somewhat from those we collected at an earlier stage in our model-building. Initially, we were interested in understanding whether income, family structure, vehicle ownership, and age had any relationship with travel behavior. Upon reviewing the NHTS data, we realized we needed to adjust some of our tract characteristic variables to better align with the ways variables are structured in NHTS. For income, we changed the variable structure from categorical brackets to a continuous number—the median income for each zone. For family structure, we opted for a binary variable that would note the presence of children in the household, regardless of the number of parents or their gender. For vehicle ownership, we found the variable to be insignificant in the first runs of the models, so we switched it out for measures of homeownership instead.

To support our choice of variables, we looked to the transportation planning literature to understand how others have analyzed the relationships between socioeconomic characteristics and travel behavior. Specifically, we noted that a 2013 paper by Boschmann and Brady found that with increasing age, travelers make fewer and shorter trips, women make fewer and shorter trips than men, and persons with disabilities make the fewest trips compared with all other persons. Equally, Agrawal et. al. found that low-income individuals have distinct travel needs and cost of travel has implications for how individuals travel. Finally, Rosenbloom finds that the presence of children changes travel behavior, more drastically for women than men.

Based on all of this, we chose to employ the following variables in our model:

• Median income (continuous variable, in thousands of dollars)
• Presence of children in the household (true or false, not further differentiated by gender or number of parents)
• Homeownership (true or false)
• Households with residents age 65 or older (true or false)

While the variables we chose were based on prior evidence outlined above, we recognize their limits in fully describing households and accurately forecasting travel behavior. For example, while both the presence of children and the presence of residents aged 65 and older tell us something about household structure, they are both proxies for more specific characteristics that define travel patterns (school or daycare enrollment in the case of children, or non-participation in the labor force in the case of people 65 and older) which could be more accurately measured and modeled if those specific data were available. Further, we chose to incorporate an indicator of homeownership as a more individualized measure of household wealth to supplement the zone-level median income.

In running the linear regression models, we kept all the variables formatted as listed above except for income, for which we applied a log-base 2 transformation (in thousands) to understand the effect of doubling one’s income rather than increasing it by a single dollar. All three models have R-squared values between 0.11 and 0.2, which means that between 11% and 20% of the variation in trip production can be attributed to the predictive variables we selected. This is in keeping with what we would expect for a model using a limited set of characteristics to predict something as complex as travel behavior. A more accurate prediction would likely require separate models for each trip purpose, using a greater number of independent variables, and many iterations of testing to determine the right combination of these variables that best fits the observed travel behavior. Equally, a more accurate model would rely on more local travel survey data, rather than subsetting the NHTS for our study area, which we have done here for the sake of time and data availability.

Estimating Trip Attractions

To estimate trip attractions for our model, we relied on the coefficients for “motorized person trips” found in NCHRP 716. Using these values, we calculated attractions for each trip type within each zone, and then balanced them with the productions to ensure an equal number of trips produced and trips attracted in the overall study area.

As expected, productions and attractions are primarily concentrated in the downtown area—attractions even more so than productions (Figure @ref(fig:density-prod), @ref(fig:density-attr)). Both generally follow the density maps of residences and employment that we created earlier in the semester.

Trip Productions are Primarily Concentrated in the Downtown Area

Trip Attractions are Even More Concentrated in the Downtown Area

Assessing Average Travel Time by Trip Purpose (based on NHTS data)

By summarizing the NHTS trips by purpose we found that Home-Based Work trips had the longest average travel time of 26.45 minutes, while both Home-Based Other and Non-Home-Based trips were significantly shorter with average times of 17.15 and 16.33 minutes respectively. These estimates aligned with our expectations that residents are typically more willing to travel farther to their jobs than for other day-to-day purposes.

Determining Travel Flows Using an Exponential Deterrence Function

Based on the observed values from NHTS data, we calibrated our exponential deterrence function to best fit those travel times. We decided to use an exponential deterrence function in keeping with our exponential accessibility decay , which reflects the same assumed value of travel time. The exponential function is written as: \[\begin{equation} F_{ijp} = e^{-mt_{ij}} \end{equation}\] where \(F_{ij}\) is the friction factor for trips with purpose p between zone i and zone j, \(t_{ij}\) is the the travel time from zone i to zone j.

We adjusted the m value for each purpose, to most closely correspond with the average travel time found in NTHS data. For Home-Based Work trips we used a value -0.06, for Home-Based Other trips we used a value of -0.18, and for Non-Home-Based trips we used a value of -0.2. The resulting estimates in our model were all within .2 minutes of the NHTS averages. Though still relatively low, the higher magnitude m values for home-based other and non-home-based trips suggest that those trip types are more sensitive to travel time in our model. This also matches our expectations that home-based work trips are the least sensitive to travel time, as they are the least “negotiable” trips a person typically takes in a given day.

Visualizing Travel Flows by Purpose and County

To better understand trip distribution within the MSA, we mapped the most frequent origin-destination pairs (those with 250 trips or more between them) by trip type. We noticed that Home-Based Other trips are the most spatially distributed across the region, while Home-Based Work trips were the most concentrated — particularly around what we believe to be the major employment centers just south of Oklahoma City.

Calculating Travel Cost

To calculate the driving cost of each trip, we estimated the straight-line distance between the origin and destination centroids, converted that distance to miles, and then used the 2023 IRS mileage reimbursement rate (0.655 dollars) to calculate the cost. The most expensive trip is about $60 to cover 91.4 miles, while the shortest trip is about 0.13 dollars to cover 0.2 miles.

We acknowledge that this is a rough approximation because it uses “as the crow flies” distance, rather than the shortest path traveled along the roadway between two centroids. We decided to take this approach because we believe that the IRS mileage rate more fully captures the cost of driving than using NHTS data to approximate cost by minute based on fuel expenses, even with this distance limitation. Equally, in the future, this method could be updated using more accurate distances along the road network.

For HOV trips, we established carpool costs using the “Carpool 2+ only—daily” assumptions from NCHRP 716, which divides the previously calculated driving cost by an average number of additional passengers.

For cost per transit trip, we had already included a transit fare when we initially created our network and skim. As an estimated average of the Embark system’s different fares, we assigned each trip a $2.00 fare with free transfers.

Mode-by-Purpose Table

In setting up the mode-by-purpose table, we noted the overwhelming share of home-based work trips that rely on single-occupancy vehicles (90 percent).

Calibration

Through trial and error, we learned the nuances of balancing out coefficients across the different modes within each trip type. We aimed to be within a 5 percentage point threshold from the observed mode share by purpose data from the NHTS.

As initial values, all constants were set to the log odds of that particular mode for that purpose from the NHTS. If the resulting predicted value was above or below the accuracy threshold, the values were adjusted manually until the result was satisfactorily close.

HBO: For SOV kept the coefficient at -0.28; we changed the coefficient for HOV from 0.167 to -0.25; and for transit we kept the coefficient at -3.52. HBW: For SOV we went from 2.26 to 0.70; HOV -2.56 to -2.00; transit -3.74 to -1.00 NHB: All mode shares were within 2 percentage points of the NHTS data shares, so we did not change the coefficients.

Visualizations

In order to understand the relationship between trip length and mode choice, we plotted the percent of trips using a particular mode (as predicted by our model) against the drive time of that trip (Figure @ref(fig:mode-split-all)). We then further subset the data by purpose to illustrate the difference in mode share for different kinds of trips (Figure @ref(fig:mode-split-hbo), @ref(fig:mode-split-hbw), @ref(fig:mode-split-nhb)).

We used drive time as our preferred metric of travel time based on the same assumption we used in the trip generation and distribution calculation — that it most often will be the shortest trip between two zones. Because there are over 130,000 individual origin-destination pairs in our matrix, we decided to create binned scatter plots which more clearly present the trend by reducing the visual noise. The bins are set at roughly 5-minute intervals in drive time, which was done by taking the max drive time of approximately 425 minutes and dividing it by 5. Within each of these bins, the mean share of each mode for all trips is calculated and presented.

While we think this approach makes the data more understandable, we acknowledge it comes with some limitations. First, because transit ridership overall is very low and there are many trips for which transit is not an option at all, taking the mean transit share results in a value of nearly 0. While this does reflect a general lack of transit use, it may also falsely give the impression that “no-one rides transit” when there are some origin-destination pairs where transit is significantly more common than others. Also, because a mean value is heavily affected by outliers, it can be a less useful or representative metric for small sample sizes. This comes up in particular for the bins of drive times above 90 minutes for which the number of trips is significantly smaller than, for example, the 5-10 minute bin.

We notice that at trips of about 45 minutes there is a slight bump in the share of HOV trips and a slight dip in the share of SOV trips. This happens again for trips of about 90 minutes. This plot suggests that it is unlikely for people to carpool for trips of 2+ hours, across all trip purposes. We also note that the bumps happen right around 15-minute intervals, suggesting an effect from people’s tendency to round time into more precise intervals.

We initially mapped this information to understand the spatial distribution of mode choice throughout our study area, too. However, it seemed repetitive of these scatter plots and did not contribute any new interpretations of our analysis. In particular, because the SOV and HOV mode shares are both approximately 40-55% of mode share for all trips, there was little range across the geography. We wonder if this lack of differentiation is a symptom of not having chosen a nested logit model.

Mode Split by Drive Time for all Trip Purposes

Mode Split by Drive Time for Home-Based Other Trips

Mode Split by Drive Time for Home-Based Work Trips

Mode Split by Drive Time for Non-Home-Based Trips

Data dictionary

Code